The mean weight of humans was estimated to be approximately 62 kgs. A scientist would like to test if the people in Toronto weigh more than 62 kgs. A sample of 40 people was obtained, and their weights W were recorded. The sample mean weight and sample standard deviation was found to be w= 63.5 kgs and sw = 3.7 lbs, respectively. a) For what parameter is w the best point estimate? b) Determine the estimated standard error of W. c) Construct a 99% confidence interval for the true mean weight of people from Toronto. d) Using the data and numbers to perform a test of hypothesis at a significance level of 0.5% of the claim that the average weight of people from Toronto is greater than 62 kgs. e) Then explain the meaning of a Type I Error, in the context of this study and give, with appropriate justification, what is known about the probability of making such a mistake in this case.